cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A341488 a(0) = 1, and for any n > 0, a(n) = A341458(a(n-1), n).

Original entry on oeis.org

1, 1, 2, 5, 8, 4, 2, 8, 1, 9, 25, 116, 8, 117, 25, 16, 1, 17, 25, 108, 8, 109, 25, 24, 1, 25, 2, 29, 8, 28, 2, 32, 1, 33, 97, 92, 8, 93, 97, 40, 1, 41, 122, 45, 8, 44, 122, 48, 1, 49, 122, 53, 8, 52, 122, 56, 1, 57, 97, 68, 8, 69, 97, 64, 1, 65, 97, 60, 8, 61
Offset: 0

Views

Author

Rémy Sigrist, Feb 13 2021

Keywords

Comments

This sequence is an analog of the factorial function for the group described in A341458, and has interesting graphical features.

Links

Crossrefs

Cf. A000142, A008590, A017077, A341458.

Programs

  • PARI
    See Links section.

Formula

Apparently:
- a(n) = 1 iff n = 1 or n belongs to A008590,
- a(n) = n iff n belongs to A017077.

A038850 Multiples of 8 that are the difference of two positive cubes.

Original entry on oeis.org

56, 152, 208, 296, 448, 488, 504, 728, 784, 936, 992, 1016, 1216, 1304, 1352, 1512, 1664, 1720, 1736, 1744, 2072, 2168, 2232, 2368, 2528, 2648, 2680, 2736, 3032, 3088, 3096, 3176, 3584, 3752, 3880, 3904, 4032, 4088, 4104, 4184, 4376, 4816, 4832, 4912
Offset: 1

Views

Author

Jeff Burch

Keywords

Crossrefs

Intersection of A008590 and A181123.

A061824 Multiples of 8 containing only the digits 0, ..., 8.

Original entry on oeis.org

0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 400, 408, 416, 424, 432, 440, 448, 456, 464
Offset: 1

Views

Author

Amarnath Murthy, May 28 2001

Keywords

Comments

Subsequence of A008590. - Michel Marcus, Nov 28 2014

Examples

			288 = 8*36 is a term containing no digit 9.
The first multiple of 8 that is not here is 96.

Crossrefs

Cf. A008590, A061818, A061819, A061820, A061821, A061822, A061823.

Programs

  • PARI
    lista(nn) = {for (n=0, nn, d = vecsort(digits(m=8*n)); if (!vecsearch(d, 9), print1(m, ", ")););} \\ Michel Marcus, Nov 28 2014

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 30 2001
Offset changed to 1 by Michel Marcus, Nov 28 2014

A260711 Numbers of the form x^2 - y^2 with x >= y; x and y are odd, x + y is a power of 2.

Original entry on oeis.org

0, 8, 16, 32, 48, 64, 96, 128, 160, 192, 224, 256, 320, 384, 448, 512, 576, 640, 704, 768, 832, 896, 960, 1024, 1152, 1280, 1408, 1536, 1664, 1792, 1920, 2048, 2176, 2304, 2432, 2560, 2688, 2816, 2944, 3072, 3200, 3328, 3456, 3584, 3712, 3840, 3968, 4096, 4352, 4608, 4864
Offset: 1

Views

Author

Arkadiusz Wesolowski, Jul 30 2015

Keywords

Comments

These binomials do not have primitive factors.

Links

Crossrefs

Subsequence of A008590.

Programs

  • Magma
    lst:=[0]; r:=4864; t:=1; d:=func; while d(t) gt t do s:=d(t); if s mod 2 eq 1 and t mod 2 eq 1 then s-:=1; end if; if s mod 2 eq 0 and t mod 2 eq 0 then s-:=1; end if; repeat; m:=(s+t)^2-(s-t)^2; if PrimeDivisors(s) eq [2] then Append(~lst, m); end if; s-:=2; until s-t lt 1; t+:=1; end while; Sort(lst); // Arkadiusz Wesolowski, Dec 19 2020

A333268 Indices of unique values in A329152.

Original entry on oeis.org

32, 240, 512, 1320, 2040, 2472, 2760, 4096, 5536, 5640, 6072, 9336, 9376, 12032, 12840, 13568, 14176, 15576, 16096, 17880, 18744, 20040, 20760, 21248, 21480, 21912, 22920, 23640, 24064, 25944, 28248, 28384, 29256, 31264, 31272
Offset: 1

Views

Author

Torlach Rush, Mar 13 2020

Keywords

Comments

a(n) == 0 (mod 8).
If a*b = k*a(n) + 1 then b - a == 0 (mod 8), 1 < a < b < a(n), 1 <= k < a(n).
gcd(k, a*b) = 1.

Examples

			32 is a term because A329152(32) = 6 and 6 occurs exactly once in A329152.
240 is a term because A329152(240) = 24 and 24 occurs exactly once in A329152.
512 is a term because A329152(512) = 126 and 126 occurs exactly once in A329152.

Crossrefs

Cf. A329152.
Subset of A008590.

A349118 Row sums of a triangle based on A261327.

Original entry on oeis.org

1, 5, 3, 18, 8, 47, 18, 100, 35, 185, 61, 310, 98, 483, 148, 712, 213, 1005, 295, 1370, 396, 1815, 518, 2348, 663, 2977, 833, 3710, 1030, 4555, 1256, 5520, 1513, 6613, 1803, 7842, 2128, 9215, 2490, 10740, 2891, 12425, 3333, 14278, 3818, 16307, 4348, 18520, 4925
Offset: 2

Views

Author

Paul Curtz, Nov 08 2021

Keywords

Comments

The following triangle has A261327 as its diagonals:
1
5
1 2
5 13
1 2 5
5 13 29
1 2 5 10
5 13 29 53
1 2 5 10 17
5 13 29 53 85
...
a(0) = a(1) = 0.
a(n)'s final digit: neither 4 nor 9.
First full bisection difference table:
0, 1, 3, 8, 18, 35, 61, 98, ... = 0, A081489 = b(n)
1, 2, 5, 10, 17, 26, 37, 50, ... = A002522
1, 3, 5, 7, 9, 11, 13, 15, ... = A005408
2, 2, 2, 2, 2, 2, 2, 2, ... = A007395
0, 0, 0, 0, 0, 0, 0, 0, ... = A000004
Second full bisection difference table:
0, 5, 18, 47, 100, 185, 310, 483, ... = c(n)
5, 13, 29, 53, 85, 125, 173, 229, ... = A078370
8, 16, 24, 32, 40, 48, 56, 64, ... = A008590(n+1)
8, 8, 8, 8, 8, 8, 8, 8, ... = A010731
0, 0, 0, 0, 0, 0, 0, 0, ... = A000004
Both bisections are cubic polynomials.
c(-n) = -c(n).

Links

Crossrefs

Cf. A002522, A005408, A007395, A078370, A081489 (first bisection).
Cf. also A008590, A010731, A261327.

Programs

  • Mathematica
    LinearRecurrence[{0, 4, 0, -6, 0, 4, 0, -1}, {1, 5, 3, 18, 8, 47, 18, 100}, 50] (* Amiram Eldar, Nov 08 2021 *)

Formula

G.f.: (5*x^5+2*x^4-2*x^3-x^2+5*x+1)/((x-1)^4*(x+1)^4).
Previous Showing 61-66 of 66 results.

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